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Ответ:

1)

Первые 5 элементов последовательности [tex]a_{1} = 4; a_{n + 1} = a_{n} + 3[/tex]

{4;7;10;13;16}

2)

Первые 5 элементов последовательности [tex]a_{1} = -2;a_{2} = 6; a_{n + 2} = 3a_{n} + a_{n + 1};[/tex]

{-2;6;0;18;18}

3)

Первые 5 элементов последовательности

[tex]a_{1} = 1;a_{2} = -2; a_{n + 2} = \dfrac{a_{n + 1}}{a_{n}};[/tex]

{1;-2;-2;1;-0,5}

Объяснение:

1)

[tex]a_{1} = 4; a_{n + 1} = a_{n} + 3[/tex]

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[tex]\boxed{a_{1} = 4}[/tex] - по условию

[tex]n = 1;[/tex]

[tex]a_{1 + 1} = a_{1} + 3[/tex]

[tex]\boxed{a_{2} = a_{1} + 3 = 4 + 3 = 7}[/tex]

[tex]n = 2;[/tex]

[tex]a_{2 + 1} = a_{2} + 3[/tex]

[tex]\boxed{a_{3} = a_{2} + 3 = 7 + 3 = 10}[/tex]

[tex]n = 3;[/tex]

[tex]a_{3 + 1} = a_{3} + 3[/tex]

[tex]\boxed{a_{4} = a_{3} + 3 = 10 + 3 = 13}[/tex]

[tex]n = 4;[/tex]

[tex]a_{4 + 1} = a_{4} + 3[/tex]

[tex]\boxed{a_{5} = a_{4} + 3 = 13 + 3= 16}[/tex]

2)

[tex]a_{1} = -2;a_{2} = 6; a_{n + 2} = 3a_{n} + a_{n + 1};[/tex]

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[tex]\boxed{a_{1} = -2}[/tex] - по условию

[tex]\boxed{a_{2} = 6}[/tex] - по условию

[tex]n = 1;[/tex]

[tex]a_{1 + 2} = 3a_{1} + a_{1 + 1}[/tex]

[tex]\boxed{a_{3} = 3a_{1} + a_{2} = 3 \cdot (-2) + 6 = -6 + 6 = 0}[/tex]

[tex]n = 2;[/tex]

[tex]a_{2 + 2} = 3a_{2} + a_{2 + 1}[/tex]

[tex]\boxed{a_{4} = 3a_{2} + a_{3} = 3 \cdot 6 + 0 = 18}[/tex]

[tex]n = 3;[/tex]

[tex]a_{3 + 2} = 3a_{3} + a_{3 + 1}[/tex]

[tex]\boxed{a_{5} = 3a_{3} + a_{4} = 3 \cdot 0 + 18 = 18}[/tex]

3)

[tex]a_{1} = 1;a_{2} = -2; a_{n + 2} = \dfrac{a_{n + 1}}{a_{n}};[/tex]

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[tex]\boxed{a_{1} = 1}[/tex] - по условию

[tex]\boxed{a_{2} = -2}[/tex] - по условию

[tex]n = 1;[/tex]

[tex]a_{1 + 2} = \dfrac{a_{1 + 1}}{a_{1}}[/tex]

[tex]\boxed{a_{3} = \dfrac{a_{2}}{a_{1}} = \dfrac{-2}{1} = -2}[/tex]

[tex]n = 2;[/tex]

[tex]a_{2 + 2} = \dfrac{a_{2 + 1}}{a_{2}}[/tex]

[tex]\boxed{a_{4} = \dfrac{a_{3}}{a_{2}} = \dfrac{-2}{-2} = 1}[/tex]

[tex]n = 3;[/tex]

[tex]a_{3 + 2} = \dfrac{a_{3 + 1}}{a_{3}}[/tex]

[tex]\boxed{a_{5} = \dfrac{a_{4}}{a_{3}} = \dfrac{1}{-2} = -0,5}[/tex]